Detection modalities that can evaluate the early stages of dental caries are indispensable. The purpose of this thesis is to evaluate the efficacy of photothermal radiometry and modulated luminescence (PTR-LUM) to non-destructively detect and quantify simulated enamel caries. Two experiments were performed based on the PTR-LUM detection mode: back-propagation or transmission-mode. Artificial demineralized lesions were created in human molars and a subset was further exposed to an artificial remineralizing solution. PTR-LUM frequency scans were performed periodically during de/re-mineralization treatments. PTR data was fitted to a theoretical model based on optical and thermal fluxes in enamel to extract opto-thermophysical parameters. Lesion validation was performed using transverse microradiography (TMR). Optical and thermal properties changed with the development and repair of the caries lesions while theory-derived thicknesses paralleled those determined microradiographically. These trends coupled with the uniqueness-of-fit of the generated parameters illustrate the efficacy of PTR- LUM to non-destructively detect and quantify de/re-mineralized lesions.

Cervix cancer affects women of all ages and causes significant morbidity and mortality. Locally advanced disease is curable with radiotherapy (RT) in about 50% of patients, although often at the expense of serious side effects. In order to improve the therapeutic ratio of tumour control versus normal tissue toxicity, conformal intensity-modulated radiotherapy (IMRT) is being investigated. However, inter- and intra-fractional motion of cervix cancer can contribute to both geographical miss of the target and overdosing of surrounding normal tissues, particularly in the setting of conformal IMRT with steep dose gradients. Defining the target volume accurately and understanding the dose consequence of these complex intra-pelvic organ dynamics during external beam radiotherapy forms the essential foundations for future treatment optimization and adaptation. This in turn will lead to improvements in tumour control and disease-free survival while minimising treatment toxicity.

Detection modalities that can evaluate the early stages of dental caries are indispensable. The purpose of this thesis is to evaluate the efficacy of photothermal radiometry and modulated luminescence (PTR-LUM) to non-destructively detect and quantify simulated enamel caries. Two experiments were performed based on the PTR-LUM detection mode: back-propagation or transmission-mode. Artificial demineralized lesions were created in human molars and a subset was further exposed to an artificial remineralizing solution. PTR-LUM frequency scans were performed periodically during de/re-mineralization treatments. PTR data was fitted to a theoretical model based on optical and thermal fluxes in enamel to extract opto-thermophysical parameters. Lesion validation was performed using transverse microradiography (TMR). Optical and thermal properties changed with the development and repair of the caries lesions while theory-derived thicknesses paralleled those determined microradiographically. These trends coupled with the uniqueness-of-fit of the generated parameters illustrate the efficacy of PTR- LUM to non-destructively detect and quantify de/re-mineralized lesions.

Cervix cancer affects women of all ages and causes significant morbidity and mortality. Locally advanced disease is curable with radiotherapy (RT) in about 50% of patients, although often at the expense of serious side effects. In order to improve the therapeutic ratio of tumour control versus normal tissue toxicity, conformal intensity-modulated radiotherapy (IMRT) is being investigated. However, inter- and intra-fractional motion of cervix cancer can contribute to both geographical miss of the target and overdosing of surrounding normal tissues, particularly in the setting of conformal IMRT with steep dose gradients. Defining the target volume accurately and understanding the dose consequence of these complex intra-pelvic organ dynamics during external beam radiotherapy forms the essential foundations for future treatment optimization and adaptation. This in turn will lead to improvements in tumour control and disease-free survival while minimising treatment toxicity.

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Optical imaging of soft biological tissue is highly desirable since it is nonionizing and provides sensitive contrast information which enables the detection of physiological functions and abnormalities, including potentially early cancer detection. However, due to the diffusive nature of light in soft biological tissue, it is difficult to achieve simultaneously good spatial resolution and good imaging depth with pure optical imaging modalities. This work focuses on the ultrasound-modulated optical tomography (UOT): a hybrid technique which combines the advantages of ultrasonic resolution and optical contrast. In this technique, focused ultrasound and optical radiation of high temporal coherence are simultaneously applied to soft biological tissue. The intensity of the sideband, or ultrasound ‗tagged‘ photons depends on the optical absorption in the region of interest where the ultrasound is focused. Demodulation of the optical speckle pattern yields the intensity of tagged photons for each location of the ultrasonic focal spot. Thus UOT yields an image with spatial resolution of the focused ultrasound — typically submillimeter — whose contrast is related to local optical absorption and the diffusive properties of light in the organ. Thus it extends all the advantages of optical imaging deep into highly scattering tissue. However lack of efficient tagged light detection techniques has so far prevented ultrasound-modulated optical tomography from achieving maturity. The signal-to-noise ratio (SNR) and imaging speed are two of the most important figures of merit and need further improvement for UOT to become widely applicable. In the first part of this work, nonlinear optics detection methods have been implemented to demodulate the ―tagged‖ photons. The most common of these is photorefractive (PR) two wave mixing (TWM) interferometry, which is a time-domain filtering technique. When used for UOT, it is found that this approach extracts not only optical properties but also mechanical properties for the area of interest. To improve on TWM, PR four wave mixing (FWM) experiments were performed to read out only the modulated light and at the same time strongly suppressing the ‗untagged‘ light. Spectral-hole burning (SHB) in a rare-earth-ion-doped crystal has been developed for UOT more recently. Experiments in Tm3 :Y3Al5O12 (Tm:YAG) show the outstanding features of SHB: large angle acceptance (etendue), light speckle processing in parallel (insensitive to the diffusive light nature) and real-time signal collection (immune to light speckle decorrelation). With the help of advanced laser stabilization techniques, two orders of magnitude improvement of SNR have been achieved in a persistent SHB material (Pr^3 :Y2SiO5) compared to Tm:YAG. Also slow light with PSHB further reduces noise in Pr:YSO UOT that is caused by polarization leakage by performing time-domain filtering.

In this dissertation, two recent problems from tomographic imaging are studied, and results from numerical simulations with synthetic data are presented. The first part deals with ultrasound modulated optical tomography, a method for imaging interior optical properties of partially translucent media that combines optical contrast with ultrasound resolution. The primary application is the optical imaging of soft tissue, for which scattering and absorption rates contain important functional and structural information about the physiological state of tissue cells. We developed a mathematical model based on the diffusion approximation for photon propagation in highly scattering media. Simple reconstruction schemes for recovering optical absorption rates from boundary measurements with focused ultrasound are presented. We show numerical reconstructions from synthetic data generated for mathematical absorption phantoms. The results indicate that high resolution imaging with quantitatively correct values of absorption is possible. Synthetic focusing techniques are suggested that allow reconstruction from measurements with certain types of non-focused ultrasound signals. A preliminary stability analysis for a linearized model is given that provides an initial explanation for the observed stability of reconstruction. In the second part, backprojection schemes are proposed for the detection of small amounts of highly enriched nuclear material inside 3D volumes. These schemes rely on the geometrically singular structure that small radioactive sources represent, compared to natural background radiation. The details of the detection problem are explained, and two types of measurements, collimated and Compton-type measurements, are discussed. Computationally, we implemented backprojection by counting the number of particle trajectories intersecting each voxel of a regular rectangular grid covering the domain of detection. For collimated measurements, we derived confidence estimates indicating when voxel trajectory counts are deviating significantly from what is expected from background radiation. Monte Carlo simulations of random background radiation confirm the estimated confidence values. Numerical results for backprojection applied to synthetic measurements are shown that indicate that small sources can be detected for signal-to-noise ratios as low as 0.1%.

This dissertation presents a 2.4 GHz wideband GFSK-modulated frequency synthesizer using two-point delta-sigma modulation (TPDSM). The two bottlenecks in this design have been rigorously investigated. One bottleneck is the nonlinear performance of the phase-locked loop (PLL). The other one is the inherent gain and delay mismatch between the two modulation points. Both nonlinear and mismatch factors dominate the modulation accuracy in the closed PLL. The proposed formulation can successfully predict the dependencies of the modulation accuracy on both factors. The comparison of the averaged frequency deviation and frequency-shift -keying (FSK) error between theory and measurement shows excellent agreement. The modulated frequency synthesizer implemented in this study can achieve a 2.5 Mbps data rate as well as a 15 £gs PLL stable time with only 2.2 % FSK error under good design and operating conditions.

This dissertation includes two topics. For the first topic about the housing price jump risk, we use EM gradient algorithms to estimate parameters of the jump diffusion model and test whether the US monthly housing price have jump risk during 1986 to 2006. Then, in order to obtain a viable pricing framework of mortgage insurance contracts, this paper uses the jump diffusion processes of Merton (1976) to model the dynamic process of housing price. Using this model, we investigate the impact of price jump risk on the valuation of mortgage insurance premium from jump intensity, abnormal volatility of jump size and normal volatility. Empirical results indicate that the abnormal volatility of jump size has the most significant impact on the mortgage insurance premium. For the second topic about the catastrophe risk, we investigate that, for catastrophic events, the assumption that catastrophe claims occur in terms of the Poisson process seems inadequate as it has constant intensity. We propose Markov Modulated Poisson process to model the arrival process for catastrophic events. Under this process, the underlying state is governed by a homogenous Markov chain, and it is the generalization of Cummins and Geman (1993, 1995), Chang, Chang, and Yu (1996), Geman and Yor (1997) and Vaugirard (2003a, 2003b). We apply Markov jump diffusion model to derive pricing formulas for catastrophe insurance products, included catastrophe futures call option, catastrophe PCS call spread and catastrophe bond. We use the data of PCS index and the annual number of hurricane events during 1950 to 2004 to test the quality of the fitting under the Markov Modulated Poisson process and the Poisson process. We reach the conclusion that the Markov Modulated Poisson process is fitter than the Poisson process and Weiner process in modeling the arrival rate of hurricane events when pricing three insurance products. Hence, if different status of climate environment has significant different arrival intensity in real economy, using jump diffusion model to evaluate CAT insurance products could cause significant mispricing.